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Railway Operations Research Seminar Put Passengers First May 3, 2016, Leuven Performance-based railway timetabling Integrating timetable construction and evaluation 3 May 2016 Rob M.P. Goverde Department of Transport and Planning Delft

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Railway Operations Research Seminar ‘Put Passengers First’ May 3, 2016, Leuven

Rob M.P. Goverde Department of Transport and Planning Delft University of Technology r.m.p.goverde@tudelft.nl

Performance-based railway timetabling

Performance-based railway timetabling

1

Integrating timetable construction and evaluation

3 May 2016

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Outline

  • Introduction
  • Timetable performance indicators
  • Timetabling design levels
  • Three-level timetabling framework
  • Case study
  • Conclusions

Performance-based railway timetabling 2

Performance-based railway timetabling

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SLIDE 3

Introduction

Current practice

  • Timetable construction either macroscopic using normative input
  • r microscopic on corridors without network focus
  • Timetable evaluation either lacking or by simulation after timetable

construction without clear feedback to timetable design

  • No well-defined timetable performance indicators

Challenge (ON-TIME project)

  • Performance-based railway timetabling

 Define timetable performance indicators  Optimize timetable with respect to these performance indicators

Performance-based railway timetabling 3

Current practice and challenge

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SLIDE 4

Timetable performance indicators

  • Travel time efficiency

 Short travel times between any OD pair, incl. running/dwell/transfer times

  • Infrastructure occupation

 Time required for a given timetable pattern on a given infrastructure

  • Stability

 Sufficient time allowances to settle delays

  • Feasibility

 Realizability: all processes realizable within their scheduled process times  Conflict-freeness: scheduled train paths are conflict free

  • Robustness

 Delay propagation behaviour kept within bounds

  • Energy-efficiency

 Timetable allows energy-efficient train operations

Performance-based railway timetabling 4

Timetable performance indicators

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SLIDE 5

Timetable peformance indicators

  • Minimum headway distance between successive trains

CIE4872: Automatic block signalling 5

Headway and blocking times

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Timetable peformance indicators

CIE4872: Automatic block signalling 6

Headway and blocking times

  • Minimum headway distance between successive trains

𝐼𝑛𝑗𝑜 = 𝑚𝑡𝑓𝑢𝑣𝑞 + 𝑚𝑡𝑗𝑕ℎ𝑢 + 𝑚𝑏𝑞𝑞𝑠𝑝𝑏𝑑ℎ + 𝑚𝑐𝑚𝑝𝑑𝑙 + 𝑚𝑑𝑚𝑓𝑏𝑠 + 𝑚𝑠𝑓𝑚𝑓𝑏𝑡𝑓

  • 𝑚𝑡𝑓𝑢𝑣𝑞

Distance over time to setup the route and clear signal

  • 𝑚𝑡𝑗𝑕ℎ𝑢

Sight distance to approach signal

  • 𝑚𝑏𝑞𝑞𝑠𝑝𝑏𝑑ℎ

Distance approach signal to main signal (block length)

  • 𝑚𝑐𝑚𝑝𝑑𝑙

Block length

  • 𝑚𝑑𝑚𝑓𝑏𝑠

Clearing distance over train length and overlap

  • 𝑚𝑠𝑓𝑚𝑓𝑏𝑡𝑓

Distance over time to release the block

R G Y

𝑚𝑡𝑓𝑢𝑣𝑞 𝑚𝑡𝑗𝑕ℎ𝑢 𝑚𝑏𝑞𝑞𝑠𝑝𝑏𝑑ℎ 𝑚𝑐𝑚𝑝𝑑𝑙 𝑚𝑑𝑚𝑓𝑏𝑠 𝐼𝑛𝑗𝑜 𝑚𝑠𝑓𝑚𝑓𝑏𝑡𝑓

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Timetable peformance indicators

CIE4872: Automatic block signalling 7

Headway and blocking times

Time Distance Occupation time Blocking time Clearing time Sight and reaction time Approach time Running time Release time Setup time 𝑚𝑡𝑓𝑢𝑣𝑞 𝑚𝑡𝑗𝑕ℎ𝑢 𝑚𝑏𝑞𝑞𝑠𝑝𝑏𝑑ℎ 𝑚𝑐𝑚𝑝𝑑𝑙 𝑚𝑑𝑚𝑓𝑏𝑠 𝑚𝑠𝑓𝑚𝑓𝑏𝑡𝑓 𝑈𝑐𝑚𝑝𝑑𝑙 = 𝑢𝑡𝑓𝑢𝑣𝑞 + 𝑢𝑡𝑗𝑕ℎ𝑢 + 𝑢𝑏𝑞𝑞𝑠𝑝𝑏𝑑ℎ + 𝑢𝑐𝑚𝑝𝑑𝑙 + 𝑢𝑑𝑚𝑓𝑏𝑠 + 𝑢𝑠𝑓𝑚𝑓𝑏𝑡𝑓

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Timetable performance indicators

Performance-based railway timetabling 8

Time Stations , signals

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Timetable performance indicators

Performance-based railway timetabling 9

Time Distance Time Distance

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Timetable design levels

Performance-based railway timetabling 10

2 Conflict-free 3 Robust 4 Resilient (incl. traffic control) Macroscopic (Normative) Stochastic Deterministic Microscopic 1 Stable (Partially) unplanned

UK DE SE CH NL FR IT

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Timetabling design levels

Level 0: Low quality

  • No conflict detection or stability analysis

Level 1: Stable timetable

  • Main characteristic: stability analysis

Level 2: Feasible (or conflict-free) timetable

  • Main characteristic: conflict detection ánd stability analysis

Level 3: Robust timetable

  • Main characteristic: robustness analysis (and stability and

feasibility) Level 4: Resilient timetable

  • Main characteristic: integration of timetabling and traffic control

 Proof that a robust timetable exists in combination with traffic management; parts of the final timetable may be computed in real- time when actual circumstances are known (delays, freight paths)

Performance-based railway timetabling 11

Clasification of the timetable design process

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Timetabling design levels

  • Higher level requires more information and advanced tools in the

timetable design process

  • Workload of dispatchers depends on timetable design level

 Level 0: Much work to do for traffic control (or low punctuality)  Level 1: Traffic control must solve structural conflicts  Level 2: Traffic control must monitor and solve small delays  Level 3: Little work for traffic control unless large delays or disruptions  Level 4: Advanced decision support to solve disturbances and delays

  • Different parts in a network may require different approach (level)

 Capacity bottlenecks

  • Focus on resilience, example: Schiphol

 Low traffic lines

  • Focus on stability

Performance-based railway timetabling 12

Clasification of the timetable design process

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Three-level timetabling framework

Performance-based railway timetabling 13

… for performance-based railway timetabling

Microscopic Module

  • Feasibility
  • Stability

Macroscopic Module

  • Efficiency
  • Robustness

Fine-Tuning Module

  • Energy efficiency
  • Robustness

Feasible?

YES NO

Stable?

NO YES

  • Bandwidths
  • Process time bounds
  • Minimum headways

MacroTT EE-profiles

railML TRC 2016

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Three-level timetabling framework

Microscopic (track section level)

  • Speed and running time computations incl. time supplements
  • Conflict detection using blocking times
  • Infrastructure occupation & stability tests by compression method
  • Constraints tightening or relaxation for macroscopic model input

Macroscopic (network level)

  • Trade-off between minimal travel times and maximal robustness
  • Also minimizing missed connections and cancelled train paths
  • Timetable precision of 5 s minimizing capacity waste

Fine-tuning (corridor level)

  • Energy-efficient speed profiles using optimal control
  • Stochastic optimization of time allowances for local trains

Performance-based railway timetabling 14

Timetabling levels

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Macroscopic model

  • Least-cost path problem over a time-extended graph (ILP)
  • Solved by randomized multi-start greedy heuristic that iteratively

schedules trains using a dynamic programming subroutine

  • Robust cost includes mean settling time from Monte Carlo delay

propagation of stochastic initial delays

Performance-based railway timetabling 15

Integer Linear Program and delay propagation

TRB 2016

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Microscopic models

  • Time-minimal, non-coasting and energy-efficient speed profiles

Performance-based railway timetabling 16

Dealing with running time supplements

1 2 3 4 5 6 7 8 x 10

4

20 40 60 80 100 120 140 Distance [m] Speed [km/h]

Time-minimal Reduced cruising speed Energy-optimal Ut Ht Ehv

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Corridor fine-tuning

Performance-based railway timetabling 17

Trade-off: time allowance in dwell or running time

TRC 2016

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Corridor fine-tuning

Performance-based railway timetabling 18

Multi-stage multi-objective dynamic programming

TRC 2016

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Corridor fine-tuning

Cost criteria at each stop (arrival/departure stage) 𝒋

  • Expected energy consumption until target station at stage 𝑗
  • Expected delay at target station from stage 𝑗
  • Expected total delay at intermediate stops from stage 𝑗
  • Each cost at stage 𝑗 depends on the time allowance decision at stage 𝑗
  • Each cost at stage 𝑗 is a recursive equation in the cost at stage 𝑗 + 1

Dynamic programming solution approach

  • Solve recursions backwards from target station back to begin
  • At each stage find the optimal time allowance at that stage that

minimizes a weighted squared sum of the three cost criteria at that stage

Performance-based railway timetabling 19

Multi-stage multi-objective dynamic progamming

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Case study

  • Infrastructure and line plan 2012
  • Two intersecting corridors

 Utrecht-Eindhoven and  Tilburg-Nijmegen

  • Hourly timetable pattern with

 2 x 8 ICs per hr  2 x 10 local trains per hr  One freight path (Ut-Ehv)  Many transfers in ‘s Hertogenbosch (and elsewhere)

Performance-based railway timetabling 20

Dutch network around ’s Hertogenbosch

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Case study

Performance-based railway timetabling 21

Microscopic and macroscopic models

Macro network 14 nodes and 14 arcs Microscopic network 1000 nodes, 1500 arcs

Timetable design norms Min running time supplement 5% Max running time supplement 30% Max journey time extension 20% Dwell time at short stops 35 s Dwell time at macro points 1-2’ Min transfer times 1-3’

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Performance-based railway timetabling 22

Ut Utl Htn Cl Gdm Zbm Ht Vg Btl Bet Ehb Ehv 10 20 30 40 50 60

Time-distance diagram for corridor Ut-Ehv

Ut Utl Htn Cl Gdm Zbm Ht Vg Btl Bet Ehv 5 10 15 20 25 30 35 40 45 50 55 60

Blocking time diagram for route of train line 3500

Distance [stations] Time [min]

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Case study

Journey time Minimum journey time [min] Scheduled journey time [min] Supplement [%] Ut-Ehv 44.9 48.2 7.3 Ehv-Ut 47.6 51.3 7.8

Performance-based railway timetabling 23

Energy consumption Energy consumption [kWh] Energy saving [%] Minimal-Time 64 395

  • Reduced cruising speed

58 800 8.7 Energy-optimal 41 667 35.3

Performance measure results

Maximum capacity consumption Infrastructure occupation time [min] Infrastructure occupation ratio [%] Corridor Ut-Ht 34.7 57.8 Station Ht 35.0 58.3

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Case study

Performance-based railway timetabling 24

Computational results: micro-macro convergence

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Case study

Performance-based railway timetabling 25

Computation time results

Iterations Mean time [s] Total [s] Initial microscopic computations 1 35 35 Micro-macro iterations 1080 Macro (1000 macro iterations) 9 80 Micro computations 9 40 Finetuning* 215 Micro computations 1 5 Energy-efficient speed profiles 1 210 Total 1330 *Excluding stochastic optimization of local trains

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Conclusions

  • Integrated method for computing optimal, stable, robust, conflict-

free and energy-efficient railway timetables

  • Modular implementation of three-level timetabling approach
  • Standardized RailML input data (Infrastructure, Rolling Stock,

Interlocking, Timetable)

  • Output in (extended) standardized RailML Timetable file with

scheduled train paths and speed profiles at section level

Performance-based railway timetabling 26

Performance-based railway timetabling

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References

1. R.M.P. Goverde, N. Bešinović, A. Binder, V. Cacchiani, E. Quaglietta,

  • R. Roberti, P. Toth (2016). A three-level framework for

performance-based railway timetabling. Transportation Research Part C, 67, 62–83 2.

  • N. Bešinović, R.M.P. Goverde, E. Quaglietta, R. Roberti (2016).

An integrated micro–macro approach to robust railway timetabling. Transportation Research Part B, 87, 14–32

Performance-based railway timetabling 27

Performance-based railway timetabling